Question

The plates of capacitor are charged to a potential difference of $100V$ and are then connected across a resistor. The potential difference across the capacitors decays exponentially with time. After $1$ second the potential difference between the plates of the capacitor is $80V$. The fraction of the stored energy which has been dissipated is :

• A. $1/5$
• B. $1/25$
• C. $9/25$
• D. $15/25$

Answer 1

The correct option is C $9/25$

We know that energy stored in a capacitor is given by
$U=\frac{C{V}^2}{2}$
let voltage initially is $V_1$
and after energy is dissipated voltage across capacitor becomes $V_2$
There Fration of energy dissipated is given by
$\frac{\Delta U}{U}=\frac{(C{V}_1^2-C{V}_2^2)/2}{C{V}_1^2/2}$
Putting $V_1=100$ and $V_2=80$
we get
$\frac{\Delta U}{U}=\frac{9}{25}$